\newproblem{lay:1_1_1}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 1.1.1}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Solve the following equation system applying row operations on the augmented matrix:
	\begin{center}
		$x_1+5x_2=7$ \\
		$-2x_1-7x_2=-5$ \\
	\end{center}
}{
  % Solution
	Let us construct the augmented matrix of the equation system
	\begin{center}
		$\left(\begin{array}{rr|r}
			1 & 5 & 7 \\
			-2 & -7 & -5
		\end{array}
		\right)$
	\end{center}
  Now we add twice row 1 to row 2
	\begin{center}
		$\left(\begin{array}{rr|r}
			1 & 5 & 7 \\
			0 & 3 & 9
		\end{array}
		\right)$
	\end{center}
	Now we divide the second row by 3
	\begin{center}
		$\left(\begin{array}{rr|r}
			1 & 5 & 7 \\
			0 & 1 & 3
		\end{array}
		\right)$
	\end{center}
	Finally, we subtract 5 times row 2 from row 1
	\begin{center}
		$\left(\begin{array}{rr|r}
			1 & 0 & -8 \\
			0 & 1 & 3
		\end{array}
		\right)$
	\end{center}
	This equation system is compatible determinate and its solution is $x_1=-8$ and $x_2=3$.
}
\useproblem{lay:1_1_1}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
